Weak convergence of random p-mappings and the exploration process of inhomogeneous continuum random trees
First Online: 14 July 2005 Received: 19 February 2004 Revised: 26 October 2004 DOI:
Cite this article as: Aldous, D., Miermont, G. & Pitman, J. Probab. Theory Relat. Fields (2005) 133: 1. doi:10.1007/s00440-004-0407-2 Abstract
We study the asymptotics of the
p-mapping model of random mappings on [ n] as n gets large, under a large class of asymptotic regimes for the underlying distribution p. We encode these random mappings in random walks which are shown to converge to a functional of the exploration process of inhomogeneous random trees, this exploration process being derived (Aldous-Miermont-Pitman 2004) from a bridge with exchangeable increments. Our setting generalizes previous results by allowing a finite number of “attracting points” to emerge. Mathematics Subject Classification (2000) 60C05 60F17 Key words or phrases Random mapping Weak convergence Inhomogeneous continuum random tree
Research supported by NSF Grant DMS-0203062.
Research supported by NSF Grant DMS-0071468.
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